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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 87v

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.81.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 86r); this page is its left half.

The machine reads it as

  1. Qvaeritur ax S(tabM + aC) sit X = lal + Jan Ergo x- al + rata et
  2. xyy = cappt pflu
  3. de
  4. +2aab
  5. In =yy = qu (apt filn)
  6. +rafp sln
  7. quos duos ipsius qu valores coincidentiando fiet ex irrationalibus aequatis sp = 2al. + ab, seu p = c (n) + ab
  8. Cellatis rationalibus fit aapp +ffln = aa l + bacln t aabh, et explicando p fiet aa Utbactnt aabt = +aa l.8 au tu+ Y aa b l. + aa bb a
  9. seu tuta ((I
  10. 44+s un
  11. +saaf In + aat(b, l = a bb
  12. = Ca
  13. 8a
  14. alberu taesc
  15. un-fslu
  16. S-a DC
  17. 5 + 4a af + 2aaff - ga dividi potest per fs- 4aa, et ideo fret
  18. C’ac
  19. aa II + raa In + aa bl + a bb + = 0 sit H- qua = ag firt aal - at tanst. - al - 0
  20. nn - ff
  21. ff. 4aa
  22. Sit +aa - f5 = ag fiet aH +4 un + abst H aabb = 0
  23. in =
  24. AS d N1 = a 1. 2 - (129) ( -= p 2 - d1 Ego d 1 - : 1 43
  25. lvco
  26. Si aquana hsfe- ageraaac sobb
  27. Y2, dt 120+ Y2
  28. F pro aequatione C scribamus 120ll + 111 In + 1100t + 100 = 0, et Ponamus
  29. Fl = C v+ ae m = 9V tah et fiet +12OCC DV + (20 ecev. + 120 aa eCC
  30. v +8
  31. vi
  32. Ut tollatur ve abetuntur C at gsi
  33. erit relatio inter c, 9, a
  34. ut tallatur v prodit similise
  35. relatio inter e, h, 8
  36. denique ut tollatur v, est prodit
  37. relatio in qua se habent c, g, a, ut e, h
  38. 120 ggvV + 2 120 a)hv + 120 aa hh
  39. 11I Cg vB+I achv + 1I aa et
  40. 111 agen
  41. 110 ac vV + 10 ac DV + 110 aa C
  42. ag vV 110 a g V 110 aa t
  43. 110 aaev
  44. pa aahv
  45. 100 aa vv Zrv0 aaGV + 100 aa
  46. consideremus
  47. aequationem 120CC +gg. CC +g9 + 11I c9 + 10 ac + 100 aao divellamus in
  48. 120 C
  49. 120 ag
  50. vael (ec gg ibi si esset 11: 120 = - 2 firret 9 2a, : a = - 2 seu q-0 quod
  51. non licet si faliamus 11: 120 = 2 fiil AX q 2a, : a = 2 seu q= 4a, sed ita foret
  52. f=0 quod eliam non licet
  53. 4. 12010
  54. 2. 120
  55. 2. 120
  56. jam siC 1II. 111 = 4. 120. 120 = 99-4a9+ 4 aa- 40a ergo faciamus 124 10 a V = cc nifiet
  57. g = = 111 c sed si eodem modo tractaremus e et h, fierent l ipsis in proportionales
  58. quod non licet ergo quia e in V (99cC = 4agce + 4aa al) sic explicabimus, ut
  59. sit qucc 1a (9- 2a) t+ Aa H et fint Y (4qce taqce t aacet 8. 2 (q.2a) acet
  60. +a =, 4aacc + 2(9 - 2a) 4aa p = aaa aatt 40 debet esse l 4C = 16 a D seu O = 4 ) D
  61. in 5q. D restat
  62. 2a
  63. H0a + 100 aa + alp. ( 20 = 110 4C+ 1o a + CC- 2(q. ca)C L + H
  64. su g = Bc 1 H 1 eC (9 2a)et + - (+ 1114. ic 4 et
  65. ab
  66. seu _g = , 1b lac + b (an) + cc - 2. 20 et 11 2 (4, - 1) 22ac 4 et
  67. =A_ bb laa) - ++ = + 2t, ita habebitur 1t qu rele aequalio divudi potent
  68. per c. sed per istam excerplam non habetur ratunaliter
  69. habetur quidem q, sed eadem 9 postea ad euc semel invenienda foret per D
  70. quando h et e tractabium ut C et 4
  71. in eri pota alsumemus +- Y C, ut evanescat cc. id quici ita Y salte irratimaliter habebitur,
  72. ideo praetabit aequadem si relinquere qualis est, et ope et quaerere 4
  73. ergo = sit D = a ent O = AHta, et pudibil 44e1p = quacc + 2(9. 2a) c. 4at + 4a4 Ht - +aa, ce - 2( -1) c t , 4 2ua, ap
  74. et hit 1 (99 Cc - 4 aqcc + 4aa cc + 2(9- 2a) cgut + 16a aH) = a (9- 29C + 4 at = 96 7 2ac
  75. seu g = +
  76. obi faliendo
  77. Fa)
  78. ce + aY seu g+ 112 C = 1(. M 4 1o nocC + 3 1 10a p) - (9geC. dage C HaB) e11. 0 C 1M M1 seu seu 11- 242
  79. scribamus ergor eet gg + ut cg = al
  80. et fiat 99 + 11I eg + W. 1I CC = MII. 1ICC
  81. 120 4. 120. 12
  82. 120
  83. aab
  84. Zaa
  85. et fiet n =
  86. seu n-
  87. 2aa
  88. (2+3)l + beg 4 + b ba4a+
  89. n
  90. + 1+ 3V
  91. =Eaal + aab

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 87v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0174?run=74